A general dynamical theory of the X-ray Laue diffraction from a homogeneously bent crystal

General properties of the rigorous solution of the problem of the X-ray dynamical Laue diffraction from a bent crystal are discussed. The solution based on the Takagi equations is formulated in the form of the Huygens-Fresnel principle. Special attention is paid to the behaviour of the quasi-classical asymptotic expansion of the exact dynamical wave fields and to the comparison of the results with those obtained by the eikonal theory. The eikonal theory is developed as a result of the application of the stationary-phase method for the evaluation of the Kirchhoff integral in accordance with the Huygens-Fresnel principle. The focusing of X-rays (the intersection of the ray trajectories and the formation of a caustic) is analysed. The generalized eikonal theory when elaborated yields that the integrated diffracted intensity from a bent crystal tends to the correct kinematical value as the strain gradient increases. For practical purposes, a simple numerical method of calculation of the integrated intensity applied in a general case of asymmetric Laue diffraction is proposed.